I went poking around the FAQ and found this page about polls. It looks like it's only the Paid or Premium Paid accounts that can do polls. I don't think they have an equivalent to a free Plus account because they're trying not to do advertising (which is what differentiates the Basic and Plus accounts at LJ; they offer more icons with Plus accounts so that you'll allow the advertising).

So, no polls unless you're a Paid account of some sort, then... :( But I guess they have to offer incentives or people wouldn't ever change from a free account. ;)

*squishes you and hands you a candy bar of your choice* (Just felt like being different and giving out something other than a cookie, lol! ;) ) ♥♥♥!!!